The 27-year-old Norwegian rider made her break for glory with 85km remaining of the 156.5km course between Geneva and Poligny in south-eastern France.
She opened up a gap during the four main mountain climbs of the day.
As the final 10km approached, the Team SD Worx-Protime rider Lotte Kopecky managed to cut Haugset's lead to 15 seconds.
But Hausget surged again to finish the stage 84 seconds ahead of the Belgian.
"I never thought winning was possible," said Hausget, who is competing in her first Tour de France.
'I had to give it everything'
"Being in this position as the winner of a stage is unreal," added the Uno-X Mobility rider.
"I thought Lotte would catch me and I was thinking that second is good but I kept on.
"The team was pushing me and I was thinking about all my teammates and everyone cheering at home and so I had to give it everything. I didn't even know that I could take the yellow jersey."
Lorena Wiebes, who won the first two stages of the race, finished more than 20 minutes behind Hausget and dropped to 67th in the general classification.
Women's Tour de France pits France's Ferrand-Prévot against history
Further up the food chain, Kim Le Court Pienaar will go into Tuesday's 21km time trial between Gevrey-Chambertin and Dijon in second place just over two minutes behind Hausget.
The 2025 champion Pauline Ferrand-Prévot lies in 10th place, two minutes and 10 seconds off the pace.
The race finishes on Sunday in Nice.
(with newswires)



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